Probability

24

The first letter can be any of the 4. The second can be any of the remaining 3. The third, either remaining, and the last, the only remaining one. This means there are 4*3*2*1=24 different arrangements.

Not necessarily. The standard deviation measures (in simplified terms) how different the numbers are from each other, while the mean is their average. If the standard deviation decreases, it means the numbers are closer to each other, it doesn't change how big the numbers are.

Minimum

The sample space consists of 2n ordered n-tuples of the form (X1, X2, ..., Xn) where each Xi = H or T.

Variance. Although usually it is the SD that is calculated from the variance.

karl pearson

41

let event is X

so

P(X)=75%=0.75

probabilty that event will not happen

P(X')=1-P(X)

P(X')=1-0.75

P(X')=0.25

so

probabilty that event will not happen is 0.25

The answer is 1 in 2^10 or 1 in 1024 or approximately 0.098%.

While there is a 50% chance of getting a heads or tails in a FAIR coin toss during each toss, there is a very low likelihood of getting 10 in row as follows:

1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1 / 1024 = approximately 0.098%.

No, average deviation cannot be negative.

Deviation is a representation of differences between numbers. A difference is always an absolute value, so the number cannot be negative (even though subtracting the deviation from an average may result in a a negative result).

It's deduction. You can find the odds of something happening by first finding out the odds of that something not happening. That is converse probability. For instance the odds of rolling a "3" on a 6 sided die. Using converse probability would be 5/6 (5 sides are not the number "3"). 6/6 (six sides in all) - 5/6 = 1/6 is the odds of rolling that "3".

It has been confirmed that in the summer time more rapes happen. This is because during the summer kids are on their summer vacations so therefore means twice the rapes.

The probability is 1 if you draw three balls without replacement.

If only one draw, it is 3/5.

At the simplest level, one would analyze the color of each marble, creating two piles of marbles (one red and one blue).

If the person was not able to see colors, they might consider using a spectrometer (spectrograph). Measuring each marble individually, each marble would be placed in the device and the wavelength would be displayed by the device. Based on the wavelength (red is in the range of 620-750nm and blue is in the range of 450-475nm), the person would still create two piles of marbles, the higher wavelength one (indicating red) and the lower wavelength one (indicating blue).

No.

there could be five possible outcomes: t= tails h= heads

t t t t 4 tails

t t t h 3 tails 1 head

t t h h 2 tails 2 heads

t h h h 1 tail 3 heads

h h h h 4 heads

A sample of size 100.

Yes. If a score is below the mean, the z score will be negative.

12

It is 10/36 = 5/18

Yes is it possible but not probable

note: please dont edit this question with stupid awnsers kthxbye

If a random variable X is distributed normally with probability distribution function p(x), then the expected value of X is

E(X) = integral of x*p(x)dx evaluated over the whole of the real line.

low head will generate low velocity (since velocity is the function of head) which results into the less discharge.

therefore the power generated will be less

hence is not suitable

An acceptable standard deviation depends entirely on the study and person asking for the study. The smaller the standard deviation, the more acceptable it will be because the less likely there are to be errors.